Direct numerical approach to one-loop amplitudes

TL;DR

This paper introduces a novel numerical method for calculating one-loop amplitudes in quantum field theory, combining contour deformation and extrapolation techniques for improved stability and efficiency.

Contribution

It develops an intuitive, stable, and robust numerical approach that calculates entire one-loop amplitudes at once, reducing numerical instabilities.

Findings

Successfully applied to $2 o (N-2) ext{gamma}$ processes

Accurately computed Higgs decay amplitude $H o extgamma extgamma$

Demonstrated stability and efficiency of the method

Abstract

We present a completely numerical method of calculating one-loop amplitudes. Our approach is built upon two different existing methods: the contour deformation and the extrapolation methods. Taking the best features of each of them, we devise an intuitive, stable and robust procedure which circumvents the problem of large cancellations and related numerical instabilities by calculating the complete amplitude at once. As a proof of concept, we use our method to calculate the $2\gamma \to (N - 2)\gamma$ benchmark process, as well as the Higgs decay amplitude $H \to \gamma \gamma$.